The noncollinear optical parametric amplification of BBO (β-BaB2O4) type-Ⅱ phase matching is theoretically investigated. The phase matching angle is calculated under different noncollinear angles. It shows that BBO type-Ⅱ phase matching has very narrow bandwidth in the simulation of the gain spectrum, which is confirmed in the numerical calculation of the parametric bandwidth. The dependence of the parametric conversion efficiency on the crystal length is simulated. The effects of the non-synchronization of the pump-pulse and signal-pulse and the shape of the incident signal-pulse on the parametric conversion effciency are also discussed. The parametric conversion efficiency has a maximum of 25% corresponding to the optimized crystal length and synchronization. The results indicate that BBO type-Ⅱ phase matching has very narrow parametric bandwidth and gain bandwidth. The approach is useful to the study of the narrow band optical parametric amplification. It also makes BBO crystal more useful in the optical parametric amplification.